Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Monotone Likelihood Ratio Property of the Poisson Signal with Three Sources of Errors in the Parameter

  • Kim, Joo-Hwan (Department of Computer Science & Statistics, Dongguk University)
  • Published : 1998.08.01
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Abstract

When a neutral particle beam(NPB) aimed at the object and receive a small number of neutron signals at the detector, it follows approximately Poisson distribution. Under the four assumptions in the presence of errors and uncertainties for the Poisson parameters, an exact probability distribution of neutral particles have been derived. The probability distribution for the neutron signals received by a detector averaged over the three sources of errors is expressed as a four-dimensional integral of certain data. Two of the four integrals can be evaluated analytically and thereby the integral is reduced to a two-dimensional integral. The monotone likelihood ratio(MLR) property of the distribution is proved by using the Cauchy mean value theorem for the univariate distribution and multivariate distribution. Its MLR property can be used to find a criteria for the hypothesis testing problem related to the distribution.

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